package tree;

/**
 * For a Maximum Segment Tree, which each node has an extra value max to store the maximum value in this node's interval.
 * Implement a modify function with three parameter root, index and value to change the node's value with [start, end] = [index, index] to the new given value. Make sure after this change, every node in segment tree still has the max attribute with the correct value.
 * 
 * Example
 * For segment tree:
 *                       [1, 4, max=3]
 *                     /                \
 *         [1, 2, max=2]                [3, 4, max=3]
 *        /              \             /             \
 * [1, 1, max=2], [2, 2, max=1], [3, 3, max=0], [4, 4, max=3]
 * if call modify(root, 2, 4), we can get:
 * 
 *                       [1, 4, max=4]
 *                     /                \
 *         [1, 2, max=4]                [3, 4, max=3]
 *        /              \             /             \
 * [1, 1, max=2], [2, 2, max=4], [3, 3, max=0], [4, 4, max=3]
 * or call modify(root, 4, 0), we can get:
 * 
 *                       [1, 4, max=2]
 *                     /                \
 *         [1, 2, max=2]                [3, 4, max=0]
 *        /              \             /             \
 * [1, 1, max=2], [2, 2, max=1], [3, 3, max=0], [4, 4, max=0]
 */
public class SegmentTreeModify {
	public void modify(SegmentTreeNode root, int index, int value) {
        if (root == null || index < root.start || index > root.end) return;
        modify(root.left, index, value);
        modify(root.right, index, value);
        root.max = root.start == root.end ? value : Math.max(root.left.max, root.right.max);
    }
}
